Street networks allow people and goods to move through cities, but they are vulnerable to disasters like floods, earthquakes, and terrorist attacks. Well-planned network design can make a city more resilient and robust to such disruptions, but we still know little about worldwide patterns of vulnerability, or worldwide empirical relationships between specific design characteristics and resilience. This study quantifies and measures the vulnerability of the street networks of every urban area in the world then models the relationships between vulnerability and street network design characteristics. To do so, we simulate over 2.4 billion trips across more than 8,000 urban areas in 178 countries, while also simulating network disruption events representing floods, earthquakes, and targeted attacks. We find that disrupting high-centrality nodes severely impacts network function. All else equal, networks with higher connectivity, fewer chokepoints, or less circuity are less vulnerable to disruption's impacts. This study thus contributes a new global understanding of network design and vulnerability to the literature. We argue that these design characteristics offer high leverage points for street network resilience and robustness that planners should emphasize when designing or retrofitting urban networks.